An extended-G geometric family

Abstract

Abstract: We introduce and study the extended-G geometric family of distributions, which contains as special models some important distributions such as the XTG (Xie et al. 2002) geometric, Weibull geometric, Chen (Chen 2000) geometric, Gompertz geometric, among others. This family not only includes distributions with bathtub and unimodal failure rate functions but provides a broader class of monotone failure rates. Its density function can be expressed as a linear mixture of extended-G densities. We derive explicit expansions for the ordinary and incomplete moments, generating function, mean deviations and Rénvy entropy. The density of the order statistics can also be given as a linear mixture of extended-G densities. The model parameters are estimated by maximum likelihood. The potentiality of the new family is illustrated by means of an application to real data. MSC: 60E05, 62P10, 62P30.